In the following ray diagram the positions of an object O, image I and two lenses `L_(1) and L_(2)` and a mirror M are given. The focal length of `L_(1)` is 10 cm. Find the focal length of `L_(2)`.

Explanation

For lens `L_(1)`,
Focal length, `f_(1)=+10cm`
Object distance, `u=-50cm`
From lens formula,
`(1)/(v)-(1)/(f)+(1)/(u)=(1)/(10)-(1)/(50)=(4)/(50)`
`rArr" "v=(50)/(4)=+12.5cm`
The image I. formed by the lens `L_(1)` acts as a virtual object for the lens `L_(2)`. The rays converging on the lens `L_(2)` become parallel after refraction and the final image is formed at infinity if there is no mirror.
For lens `F_(2)`.
Object distance, `u=12.5-5`
`=+7.5cm`
Image distance, `v=oo`
From lens formula, focal length is given by
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/(oo)-(1)/(7.5)`
`rArr" "f=-7.5cm`